In standard axiomatic set theory, by the principle of extensionality, two sets are equal if they have the same elements (that is, neither of them has an element not in the other). As a result, there can be only one set with no elements, hence the usage of "the empty set" rather than "an empty set".

citation

Wikipedia contributors. (2023, October 28). Empty set. In Wikipedia, The Free Encyclopedia. Retrieved October 31, 2023, from https://en.wikipedia.org/w/index.php?title=Empty_set&oldid=1182337108

Seattle (Wikipedia) Seattle (/siˈætəl/ see-AT-əl) is a seaport city on the West Coast of the United States. It is the seat of King County, Washington. With a 2022 population of 749,256 it is the largest city in both the state of Washington and the Pacific Northwest region of North America. The Seattle metropolitan area’s population is 4.02 million, making it the 15th-largest in the United States. Its growth rate of 21.1% between 2010 and 2020 made it one of country’s fastest-growing large cities.

Empty set (Wikipedia) In mathematics, the empty set is the unique set having no elements; its size or cardinality (count of elements in a set) is zero. Some axiomatic set theories ensure that the empty set exists by including an axiom of empty set, while in other theories, its existence can be deduced. Many possible properties of sets are vacuously true for the empty set.